I'm confused by your mention of "difference between head/abdomen circumference." I googled it & found this:
"Ultrasound measurement of just the fetal abdominal circumference provides a reasonable estimate of the risk for intrauterine growth retardation among term babies when other measures are unavailable"
Are they concerned about fetal development in any way? (I would think IUGR isn't an issue if they're talking big baby.)
Or is this ONLY about elective CS PURELY for "big baby/CPD/Shoulder dystocia"?
If the latter, well, even ACOG doesn't recommend CS for suspected fetal macrosomia!
The ACOG practice bulletin discusses the following clinical considerations:
...... CESAREAN DELIVERY.
... Nonetheless, the results of these reports, along with published cost-effectiveness data, do not support prophylactic cesarean delivery for suspected fetal macrosomia with estimated weights of less than 5,000 g (11 lb),"
Furthermore, Late-term US are notoriously inaccurate and can be off by up to 2#!!!
Finally, I've never heard anything of a baby not being engaged at 40W to be a problem at all. Not in the least. As a matter of fact, vaginal exams to assess baby's position (i.e. "station" + or - 3, etc.) as well as cervical dilation & effacement in late pregnancy aren't evidence-based because there's just no need to know that info. The ONLY value in VEs to acquire that info is if you want to get a Bishop's score to consider being induced. But other than that, those three numbers don't tell you anything about when the baby will arrive.
From that same link:
"INDUCTION OF LABOR.
In cases of term patients with suspected fetal macrosomia, current evidence does not support early induction of labor."
Induction is also particularly risky for first-time moms with a CS risk as high as 50%.
I just browsed this but it looks like a good article:
The idea of a CPD diagnosis without labor particularly pisses me off. They are essentially saying, "This baby won't fit through your pelvis." Well ya know what? THEY ARE RIGHT... but the baby is not SUPPOSED TO fit through the pelvis until the woman is in labor. Ugh! & you can help that process along by doing things like being upright, certain movements, and I think even certain pelvic squeezes.
Unless she had the disease Rickets (which is very rare in the developed world these days), I can't see logic behind a prenatal diagnosis of CPD for a first-timer.
However, if there is any sort of truth to the big baby/small pelvis concerns it is that much more ESSENTIAL that she have good care providers who KNOW the value of movement & upright positions to help her pelvis open. :( The typical American approach to birth could certainly CAUSE CPD to become a reality (leaving those HCPs with a self-fulfilling prophecy, thinking they were right all along, when in reality they failed to take measures to HELP the birth progress naturally.)
Based on what you've already posted, I think it's reasonable to suspect these HCPs don't know the value of proper support in labor to help a pelvis open naturally, so if she doesn't go for the CS, I'd implore her to get a very good, very experienced, very strong-willed doula.